(2x-5)(2x-5)=(x-1)(x-1)

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Solution for (2x-5)(2x-5)=(x-1)(x-1) equation: 


Simplifying
(2x + -5)(2x + -5) = (x + -1)(x + -1)

Reorder the terms:
(-5 + 2x)(2x + -5) = (x + -1)(x + -1)

Reorder the terms:
(-5 + 2x)(-5 + 2x) = (x + -1)(x + -1)

Multiply (-5 + 2x) * (-5 + 2x)
(-5(-5 + 2x) + 2x * (-5 + 2x)) = (x + -1)(x + -1)
((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) = (x + -1)(x + -1)
((25 + -10x) + 2x * (-5 + 2x)) = (x + -1)(x + -1)
(25 + -10x + (-5 * 2x + 2x * 2x)) = (x + -1)(x + -1)
(25 + -10x + (-10x + 4x2)) = (x + -1)(x + -1)

Combine like terms: -10x + -10x = -20x
(25 + -20x + 4x2) = (x + -1)(x + -1)

Reorder the terms:
25 + -20x + 4x2 = (-1 + x)(x + -1)

Reorder the terms:
25 + -20x + 4x2 = (-1 + x)(-1 + x)

Multiply (-1 + x) * (-1 + x)
25 + -20x + 4x2 = (-1(-1 + x) + x(-1 + x))
25 + -20x + 4x2 = ((-1 * -1 + x * -1) + x(-1 + x))
25 + -20x + 4x2 = ((1 + -1x) + x(-1 + x))
25 + -20x + 4x2 = (1 + -1x + (-1 * x + x * x))
25 + -20x + 4x2 = (1 + -1x + (-1x + x2))

Combine like terms: -1x + -1x = -2x
25 + -20x + 4x2 = (1 + -2x + x2)

Solving
25 + -20x + 4x2 = 1 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
25 + -1 + -20x + 2x + 4x2 + -1x2 = 1 + -2x + x2 + -1 + 2x + -1x2

Combine like terms: 25 + -1 = 24
24 + -20x + 2x + 4x2 + -1x2 = 1 + -2x + x2 + -1 + 2x + -1x2

Combine like terms: -20x + 2x = -18x
24 + -18x + 4x2 + -1x2 = 1 + -2x + x2 + -1 + 2x + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
24 + -18x + 3x2 = 1 + -2x + x2 + -1 + 2x + -1x2

Reorder the terms:
24 + -18x + 3x2 = 1 + -1 + -2x + 2x + x2 + -1x2

Combine like terms: 1 + -1 = 0
24 + -18x + 3x2 = 0 + -2x + 2x + x2 + -1x2
24 + -18x + 3x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
24 + -18x + 3x2 = 0 + x2 + -1x2
24 + -18x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
24 + -18x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + -6x + x2) = 0

Factor a trinomial.
3((2 + -1x)(4 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {2, 4}

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